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Delays in activity-based neural networks.

Stephen Coombes1, Carlo Laing

  • 1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. stephen.coombes@nottingham.ac.uk

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 17, 2009
PubMed
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This study investigates how discrete delays impact Wilson-Cowan neural network dynamics. Delays can generate network rhythms, leading to synchronous or anti-synchronous oscillations and even chaotic behavior in neural populations.

Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Neuroscience

Background:

  • The Wilson-Cowan model is a foundational activity-based neural network model.
  • Discrete delays are crucial in neural signaling and network dynamics.
  • Understanding delay effects is key to explaining emergent network rhythms.

Purpose of the Study:

  • To analyze the influence of two distinct discrete delays on Wilson-Cowan neural network dynamics.
  • To explore how delays contribute to the generation of network rhythms.
  • To investigate the emergence of synchronous, anti-synchronous, and chaotic behaviors.

Main Methods:

  • Linear stability theory to identify onset of oscillations.
  • Analysis of Heaviside nonlinearity for firing rates.

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  • Numerical bifurcation analysis and direct simulations for sigmoidal nonlinearities.

    • Main Results:

    • Delays can destabilize fixed points, inducing oscillatory behavior.
    • Emergent oscillations can be synchronous or anti-synchronous based on network architecture.
    • Parameter windows supporting chaotic behavior were identified for smooth nonlinearities.

    Conclusions:

    • Discrete delays play a significant role in shaping neural network dynamics and rhythm generation.
    • The interplay of delays and network architecture dictates oscillation synchrony.
    • Delays are implicated in complex phenomena like bursting oscillations and chaos.